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Abstract
We provide new upper and lower bounds for the Betti numbers of nilpotent Lie algebras. As an application, we prove the toral rank conjecture (TRC) for nilmanifolds of dimension at most 14 and for a small class of coformal spaces. We also give a new, direct proof of the result of Deninger and Singhof that the TRC is true for 2‐step nilpotent Lie algebras.